US 7154969 B2 Abstract A method for shared estimation of parameters (ε, φ, |C
_{1}|, C_{0}, α, Δω) is described, which together with an error vector e(k), describe the connection between a digitally modulated reference signal inputted to a transmission channel and a received receiver signal z(k) which is at an end of the transmission channel. The method includes the following steps: forming the error vector e(k) in dependence of the parameters (ε, φ, |C_{1}|, C_{0}, α, Δω), a reference signal s(k), and the receiver signal z(k); linearizing the error vector e(k); substituting a real parameter of the linearized error vector through components of a estimation vector, wherein a substituted error vector is produced; inserting the substituted error vector into the cost function; and determining the estimation vector through gradient development of the cost function and subsequently setting the gradient to zero.Claims(12) 1. A method for shared estimation of a plurality of transmission channel parameters for use of determining an error-vector magnitude, the plurality of transmission channel parameters with an error vector e(k) describing the relationship between a digitally modulated reference signal s(k) inputted to a transmission channel and a received receiver signal z(k) which is at a receiving end of the transmission channel, where k is a symbol number, said method comprising the steps of:
inputting the reference signal s(k) at a transmitting end of the transmission channel and receiving the received receiver signal z(k) at the receiving end of the transmission channel;
forming the error vector e(k) in dependence of the plurality of transmission channel parameters, the reference signal s(k), and the receiver signal z(k);
linearizing the error vector e(k);
substituting each real parameter of the linearized error vector through a corresponding real component of an estimation vector {circumflex over (x)} to obtain a form of
wherein the real components of the estimation vector {circumflex over (x)} is defined as a real estimation value vector x=(x
_{1}x_{2}x_{3}x_{4}x_{5}x_{6}x_{7})^{r }, x_{i }is the i^{th }real parameter of the real estimation vector x, f_{i}(k) is the i^{th }function corresponding to x_{i}, and i=1–7;inserting the form
into a cost function,
wherein K is a symbol number within an evaluation area; and
determining the estimation vector {circumflex over (x)} through gradient development of the cost function and subsequently setting the gradient to zero.
2. The method according to
3. The method according to
_{1}|, a constant level shift C_{0, }an amplitude change αand a frequency shift Δω, which determine the reference signal s(k) on the transmission channel, and wherein C_{1 }is a complex amplification.4. The method according to
_{1}|, C_{0}, α, Δω), the reference signal s(k), and the received receiver signal z(k), has a form ofwherein T
_{s }is a symbol period, and a signal sequence, is in a signal pulse, and is present to time points k·T_{s}, and wherein C_{1}=|C_{1}|·e^{j·φ}is applied.5. The method according to
wherein s
_{d}(k) is a normed derivative of s(k).6. The method according to
| C _{1}|=1/x _{1} Δω T _{s} =x _{2} ·|C _{1}|Δφ= x _{3} ·|C _{1}|C _{1} =|C _{1} |·e ^{jφ} C _{0} =C _{1}·(x _{4} +j·x _{5})ε=x _{6} α= x _{7} ·|C _{1}|are made, to produce the real estimation value vector:
x=(x _{1} x _{2} x _{3} x _{4} x _{5} x _{6} x _{7})^{T}.7. The method according to
8. The method according to
9. The method according to
10. A computer program with program code resources to perform all of the steps according to
11. A computer program with program code resources to perform all of the steps according to
12. A computer program product, having program code resources stored on a machine readable medium, to perform all of the steps according to
Description This nonprovisional application claims priority under 35 U.S.C. § 119(a) on Patent Application No. 101 57 247.6 filed in Germany on Nov. 22, 2001, which is herein incorporated by reference. 1. Field of the Invention The present invention relates to a method and computer program for shared estimation of parameters, in particular to the determination of “Error Vector Magnitude” (hereinafter “EVM”). 2. Description of the Background Art The “Error Vector Magnitude” (EVM) is used often, to estimate the linearity of a digitally modulated mobile radio system. For Example, the standard “GSM 05.05, version 8.5.0, Draft ETSI EN 300 910 V.8.5.0, (2000–07), Annex G” (hereinafter “the standard”) defines the requirements on the EVM for the 8-PSK GSM EDGE-System. However, the standard does not define algorithms in order to determine the EVM. The following allocations are applied: - T
_{s}: symbol period;- The sequence of the configuration, are present before the symbol clock of the time points kT
_{s}.
- The sequence of the configuration, are present before the symbol clock of the time points kT
- s(k): reference signal: is a trouble-free input signal after the measurement filter in the receiver to the symbol-time points kT
_{s}; - e(k): error vector;
- ε: resultant time shift due to a non-ideal estimation of the preceding coarse time shift estimation;
- C
_{1}: complex amplification (gain) of the measurement signal; - C
_{0}: constant level of a (DC) offset in the measurement signal; and - w=e
^{α+jΔωT}^{ s }α describes the change in amplitude of the measurement signal, which, for example, because of the heating up of the amplifier, causes a higher signal level to arise within the bursts.- Furthermore, through Δω the resultant frequency shift is modeled due to the preceding non-ideal coarse frequency estimation.
From the reference signal s(k), the following received signal z(k) results:
The error vector e(k) is determined by:
In view of this model, a total of seven real parameters have to be estimated. It is noted that the time shift ε, in view of the excessive sampled sequence, is to be understood to fulfill the sample theorem. The “Error-Vector magnitude” (EVM) is calculated over a burst and is defined as follows:
To determine the “Error-Vector magnitude” (EVM), the parameters ε, C The article “A Method for Computing Error Vector Magnitude in GSM EDGE Systems—Simulation Results,” IEEE Communications Letters, VOL. 5, NO. 3, March 2001, pages 88 to 91, discloses a method to determine the parameters ε, C It is, therefore, an object of the present invention to provide a method to commonly estimate several parameters, which together with the error vector describes the connection between a digitally modulated reference signal fed through the transmission channel and a received signal that is received at the end of the transmission channel, which method utilizes a fewer number of iterations and converges quickly. The invention also provides a computer program to execute the method. A preferred embodiment of the method of the invention, uses a linearization and a substitution to calculate the parameters analytically. Because of linearization, a minor error arises. Through iterative repetition, the linearization error can be desirably reduced. In the norm, two iterations are sufficient. These are substantially fewer iterations than those needed in the conventional method. Further scope of applicability of the present invention will become apparent from the detailed description given hereinafter. However, it should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description. The present invention will become more fully understood from the detailed description given herein below and the accompanying drawings which are given by way of illustration only, and thus, are not limitive of the present invention, and wherein: The estimation method according to a preferred embodiment of the invention is described herein below, wherein estimated parameters are a time shift ε, a phase shift φ, a amplification |C The estimated parameters are determined through the minimization of the cost function:
wherein K is the symbol number within the evaluation area (“useful part,” e.g. a burst). Generally, in this invention, a test parameter is represented by a “snake” and the estimated parameter is represented by a “roof,” that is, {circumflex over (x)} describes generally the parameter that is to be estimated, and {tilde over (e)}(k) describes a therefrom resultant test-error vector. Subsequently, the estimation according to a preferred embodiment is deduced. In the deduction, for the purpose of improving the overview, no iteration specific nomenclature is used. In C By substituting the equations (5) and (6) into equation (2) the error vector is determined
Due to the preceding coarse estimation, a linearization in equation (7) is allowable: for a complex x, via Taylor series expansion, e Furthermore, the time shift s(k−ε) is linearized by
It is noted that the normed derivative s By substituting equations (8) and (9) into equation (7), the linearization error vector is obtained:
Through substitution, the real parameters x
The real estimation value vector is defined through:
Through conversion, according to equation (11), the estimation values to be focused on from the estimation value vector x are determined according to:
Through gradient development, the cost function L(x) and the subsequent zero setting of the gradient, the estimation value vector {circumflex over (x)} is obtained according to:
By substituting equation (13) into equation (15) the Matrix M and the Vector b is obtained, which is shown in By linearizing equation (8) and equation (9), the error-prone to the estimation vector {circumflex over (x)} in equation (14) is negligible. According to a preferred advancement of the method of the invention, several iterations are performed. The error can be desirably reduced through several iterations. In the norm, the error is negligible after 2 iterations. The following is applied:
On the inputs From the over-sampled reference signal s For the estimation, only the valid symbols (“useful symbols”) are used, wherefore a slotting before the estimation must be performed. In the over-sampled input signals a pre-run and post-run are needed. The reason therefore is that a FIR (finite impulse response) filter The following points have to be thereby regarded: Only the linearized estimation parameters ({circumflex over (ε)}, ŵ, and {circumflex over (φ)}) are compensated at the beginning of a new iteration. For the linearized estimation parameters it applies that: the linearized (refined)-estimation value of the loop-ed iteration are {circumflex over (ε)}
With these instantaneous total estimation values, the measurement sequence will be compensated in the next iteration. With every new iteration, the measurement sequence z The non-linearized estimation values (Ĉ It is to be heeded, that the estimated time shift {circumflex over (ε)} is not compensated in the reference signal, but in the measurement signal (input signal). Through which, according to the measurement regulation, the standards are achieved, in that the measurement signal is interpolated on the inter-symbol-interference-free symbol time point. After the last iteration loop-iteration, the equation (16) of the resultant total estimation value of the linearized parameter is present. The non-linearized parameters are taken from the calculation of the last iteration. Finally, the compensated measurement sequence z
When the method according to the invention is utilized in a CDMA (Code Division Multiple Access) signal, the reference signal comprises a plurality of superimposed partial signals from different code channels and always one parameter for every partial signal describes the different amplifications of the different code channels. The amplification-parameter of the different partial signals is estimated simultaneously with the method according to the invention. The invention being thus described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the invention, and all such modifications as would be obvious to one skilled in the art are to be included within the scope of the following claims. Patent Citations
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